Non-Abelian topological charges are discussed in three-band models protected
by \(PT\)  symmetry[1]}, [2]}, [3]}, [4]}, [5]} or \(C_{2}T\)  symmetry[6]}, [7]}. They are realized in nodal line semimetals[1]}, [2]}, [4]}, [5]}, [12]}, [13]}, [14]} in three dimensions and
Weyl points[6]} in two dimensions. Non-Abelian topological
insulators in one dimension are studied for three-band models[3]} and
four-band models[17]}. They are experimentally observed in photonic
systems[4]}, [7]}, phononic systems[13]}, [21]} and
transmission lines[3]}, [17]}. In addition, a generalization to
multi-band theories is proposed in nodal line semimetals[1]}. As
far as we aware of, there is no study on non-Hermitian non-Abelian
topological phases so far.
